In coding of an audio signal and an acoustic signal, a method for performing coding based on a predictive coefficient obtained by performing linear predictive analysis on the inputted audio signal and acoustic signal is widely used (see, for example, Non-patent literatures 1 and 2).
In Non-patent literatures 1 to 3, a predictive coefficient is calculated by a linear predictive analysis apparatus illustrated in FIG. 11. The linear predictive analysis apparatus 1 comprises an autocorrelation calculating part 11, a coefficient multiplying part 12 and a predictive coefficient calculating part 13.
An input signal which is an inputted digital audio signal or digital acoustic signal in a time domain is processed for each frame of N samples. An input signal of a current frame which is a frame to be processed at current time is set at Xo(n) (n=0, 1, . . . , N−1). n indicates a sample number of each sample in the input signal, and N is a predetermined positive integer. Here, an input signal of the frame one frame before the current frame is Xo(n) (n=−N, −N+1, . . . , −1), and an input signal of the frame one frame after the current frame is Xo(n) (n=N, N+1, . . . , 2N−1).
[Autocorrelation Calculating Part 11]
The autocorrelation calculating part 11 of the linear predictive analysis apparatus 1 obtains autocorrelation Ro(i) (i=0, 1 . . . . , Pmax, where Pmax is a prediction order) from the input signal Xo(n) using equation (11) and outputs the autocorrelation. Pmax is a predetermined positive integer less than N.
                    [                  Formula          ⁢                                          ⁢          1                ]                                                                                  R            o                    ⁡                      (            i            )                          =                              ∑                          n              =              i                                      N              -              1                                ⁢                                                    X                o                            ⁡                              (                n                )                                      ×                                          X                o                            ⁡                              (                                  n                  -                  i                                )                                                                        (        11        )            
[Coefficient Multiplying Part 12]
Next, the coefficient multiplying part 12 obtains modified autocorrelation R′o(i) (i=0, 1, . . . , Pmax) by multiplying the autocorrelation Ro(i) outputted from the autocorrelation calculating part 11 by a coefficient wo(i) (i=0, 1, . . . , Pmax) defined in advance for each of the same i. That is, the modified autocorrelation function R′o(i) is obtained using equation (12).[Formula 2]R′o(i)=Ro(i)×wo(i)  (12)
[Predictive Coefficient Calculating Part 13]
Then, the predictive coefficient calculating part 13 obtains a coefficient which can be converted into linear predictive coefficients from the first-order to the Pmax-order which is a prediction order defined in advance using the modified autocorrelation R′o(i) outputted from the coefficient multiplying part 12 through, for example, a Levinson-Durbin method, or the like. The coefficient which can be converted into the linear predictive coefficients comprises a PARCOR coefficient Ko(1), Ko(2), . . . , Ko(Pmax), linear predictive coefficients ao(1), ao(2), . . . , ao(Pmax), or the like.
International Standard ITU-T G.718 which is Non-patent literature 1 and International Standard ITU-T G.729 which is Non-patent literature 2 use a fixed coefficient having a bandwidth of 60 Hz obtained in advance as a coefficient wo(i).
Specifically, the coefficient wo(i) is defined using an exponent function as in equation (13), and in equation (13), a fixed value of f0=60 Hz is used. fs is a sampling frequency.
                    [                  Formula          ⁢                                          ⁢          3                ]                                                                                                w              o                        ⁡                          (              i              )                                =                      exp            ⁡                          (                                                -                                      1                    2                                                  ⁢                                                      (                                                                  2                        ⁢                                                                                                  ⁢                        π                        ⁢                                                                                                  ⁢                                                  f                          0                                                ⁢                        i                                                                    f                        s                                                              )                                    2                                            )                                      ,                  i          =          0                ,        1        ,        …        ⁢                                  ,                  P          max                                    (        13        )            
Non-patent literature 3 discloses an example where a coefficient based on a function other than the above-described exponent function is used. However, the function used here is a function based on a sampling period (corresponding to a period corresponding to fs) and a predetermined constant a, and a coefficient of a fixed value is used.